BMC Neuroscience
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Poster presentation
Experimenting the variational definition of neural map computation Olivier Rochel*, Pierre Kornprobst and Thierry Vieville Address: Odyssee Lab, INRIA Sophia-Antipolis, France Email: Olivier Rochel* -
[email protected] * Corresponding author
from Sixteenth Annual Computational Neuroscience Meeting: CNS*2007 Toronto, Canada. 7–12 July 2007 Published: 6 July 2007 BMC Neuroscience 2007, 8(Suppl 2):P179
doi:10.1186/1471-2202-8-S2-P179
Sixteenth Annual Computational Neuroscience Meeting: CNS*2007
William R Holmes Meeting abstracts – A single PDF containing all abstracts in this Supplement is available
here http://www.biomedcentral.com/content/pdf/1471-2202-8-S2-info.pdf
© 2007 Rochel et al; licensee BioMed Central Ltd.
Variational formulation to spiking neural networks: A top-down approach We bring new insights to better understand the link between spiking neural networks and variational approaches. To do so, we consider two simple visual tasks formulated as variational approaches, related to linear/ non-linear filtering [1] and input selection: Image denoising via edge-preserving smoothing, and focus of attention via a winner-take-all mechanism. Variational approaches, which refer to an energy minimization formulation, are defined in a continuous setting. Our goal is to show how spiking neural networks can be used to minimize those energies. Based on some recent advances [2,3], including spiking neurons [4], the key point is to understand the relation between smoothness constraints and cortical activity diffusion (as observed with extrinsic optical imaging). In particular, we will focus on the two following issues:
Results and discussion Input images, encoded by means of a simple latency code, are processed by a network of spiking neurons generated from the variational description of the task. A simple temporal coding scheme is used in this initial study, the underlying idea being to analyze the possible role of synchrony as a support for diffusing information [5]. A step further, this relates to more general forms of computation in the brain, in terms of propagation of information, neural coding. It has also being linked [3] to modulation of a feed-forward processing track by various feedback mechanisms.
Diffusion Depending on the task, and given the underlying neural circuitry and computational power, how far, and how fast should local information be transmitted (e.g., intensity, local gradient, local movement)? Feedback How can different information pathways, associated with different processing tasks, interact?
Figuredenoising Image actions (nearest 1 by neighbors) a spiking neural network with local interImage denoising by a spiking neural network with local interactions (nearest neighbors).
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BMC Neuroscience 2007, 8(Suppl 2):P179
Acknowledgements This work was partially supported by the EC IP project FP6-015879, FACETS.
References 1.
2. 3. 4. 5.
Aubert G, Kornprobst P: Mathematical problems in image processing: partial differential equations and the calculus of variations. In Applied Mathematical Sciences Volume 147. Springer-Verlag; 2006. Cottet G-H, El Ayyadi M: Volterra type model for image processing. IEEE transactions on image processing 1998:7. Viéville T, Kornprobst P: Modeling cortical maps with feedbacks. Int Joint Conf on Neural Networks 2006. Kornprobst P, Chemla S, Rochel O, Vieville T: A 1st step towards an abstract view of computation in spiking neural networks. in Proc NeuroComp 2006. Singer W: Neuronal synchrony: a versatile code for the definition of relations? Neuron 1998, 24:49-65.
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